Helstrom minimum-error trace-norm formula

For quantum states $\rho$ and $\sigma$ with equal prior probabilities, the minimum average error probability over binary hypothesis tests is $P^*(\rho,\sigma)=\frac12(1-D(\rho,\sigma))$, where $D(\rho,\sigma)=\frac12\|\rho-\sigma\|_1$ is the normalized trace distance.